bge character stops moving when it jumps
If you enable "Add" on all your motion actuators, you will get behavior closer to what you'd expect. With the logic how you have it now, when you push W, A, S, D or Space, the corresponding motion actuator sets the new location of the cube, based on the old location. The differences in location is what you have in the motion actuators. Because of this, only one can run at once - they are all trying to run at the same time, and they are all trying to set the cube's new location based on what they have filled in, which is different for each object.

However, if  you set them to add, each one will add or subtract from the cube's location, instead of trying to set it. When you press Space, while holding forward, instead of the BGE taking the cubes location, adding to it along the Z, and setting the new location, it will simply add to the cube's Z location, creating the expected behavior.



In addition to having your cube able to move and jump at the same time, if you enable the "Add" setting on your other motion actuators, your cube will be able to move diagonally.